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Abstract

Multi-agent networks are often modeled via interaction graphs, where the nodes represent the agents and the edges denote direct interactions between the corresponding
agents. Interaction graphs have significant impact on the robustness of networked systems. One family of robust graphs
is the random regular graphs. In this paper, we present a locally
applicable reconfiguration scheme to build random regular graphs through self-organization. For any connected initial graph, the proposed scheme maintains connectivity and the average degree while minimizing the degree differences and
randomizing the links. As such, if the average degree of the initial graph is an integer, then connected regular graphs are realized uniformly at random as time goes to infinity.